General Motors, the Detroit carmaker rescued by the US government, is set to pay back around $7bn of the $58bn (£36bn) it owes the American taxpayer following a public share offering.

Wall Street sources said that the listing, which is expected to be announced within days, would raise between $9.5bn and $10.5bn. The funds would mostly "go to reducing the US and Canadian governments' stake in GM" – valuing the company at upwards of $50bn, roughly equivalent to its rival Ford Motor Company.

Craig Fitzgerald, a motor analyst at advisory firm Plante & Moran in Detroit, said: "There are a number of reasons why this is happening now. First, GM has good things to talk about and its main models have been well received in all markets except Europe.

"Second the government wants out. This has been a terrible embarrassment for the administration. Third, the board and management want a transition as soon as possible to a more normal structure. But more of a driver is to get the process [of paying back the government] started. This is a small down payment. The longer that takes to get started, the longer the whole process takes."

Some market watchers suggested that the flotation would be slightly underpriced to help the share price rally ahead of future offers. However, Guy LeBas, chief fixed income strategist with Janney Capital Markets, said: "The valuation is more or less within [a fair] range. The US government will still be the biggest shareholder after this re-PO – IPO doesn't seem a fitting term for a 100-year-old formerly public company – so it will have an interest in the price rallying. But the investment banks have a fiduciary duty to get the best level they can sell it at."

To drum up interest, the carmaker is believed to be planning to promote its growing business outside North America and Europe, which has been based on a focus on its four key brands: Chevrolet, Cadillac, Buick, and GMC. The company also retains its Opel and Vauxhall brands in Europe, but sold its Saab marque to Dutch luxury carmaker Spyker for $74m earlier this year.

The valuable assets that the company owned were subsequently bought out of pre-pack administration, with the rump left in a company known as Motors Liquidation Corp. Apart from the US and Canadian governments, about 10% of "new GM" will be owned by the bondholders of MLC, while the United Auto Workers union holds about a sixth of the company. The UAW is also believed to be selling some of its shares.

Separately, GM is raising upwards of $2bn in a sale of preferred shares held by the US Treasury – while US reports suggest that the listing is due to be priced on 17 November and begin trading in New York and Toronto the next day.

Last week GM negotiated a $5bn revolving credit facility with a group of banks in order to improve its financial flexibility ahead of the listing.

General Motors was founded in 1908 by William "Billy" Durant, a manufacturer of horse-drawn vehicles in Flint, Michigan. At its inception, GM held only the Buick Motor Company, but over the next few years it was to acquire more than 20 other motor companies, including Cadillac.

In 1929 the company bought Germany's Opel, which had begun life as a manufacturer of sewing machines and bicycles.